An Exploratory Approach to Kaplansky's Lemma
Leads to a Generalized Resultant
1997
The familiar resultant of two polynomials is the determinant of a
matrix, the so-called Sylvester matrix, formed in a very simple way
from the polynomials' coefficients. The resultant is nonzero if and
only if the two polynomials are relatively prime. This is because
the resultant is in fact the product of all differences of roots
of the two polynomials (in a splitting field). In this paper, we do
something similar for several polynomials. However, the nonzero
entries in the associated matrix, rather than being the coefficients
themselves (as in the Sylvester matrix), are polynomials in
these coefficients.
